By Kamalika Chaudhuri, CLAUDIO GENTILE, Sandra Zilles

This booklet constitutes the complaints of the twenty sixth overseas convention on Algorithmic studying concept, ALT 2015, held in Banff, AB, Canada, in October 2015, and co-located with the 18th foreign convention on Discovery technology, DS 2015. The 23 complete papers awarded during this quantity have been rigorously reviewed and chosen from forty four submissions. moreover the publication comprises 2 complete papers summarizing the invited talks and a couple of abstracts of invited talks. The papers are geared up in topical sections named: inductive inference; studying from queries, educating complexity; computational studying concept and algorithms; statistical studying concept and pattern complexity; on-line studying, stochastic optimization; and Kolmogorov complexity, algorithmic details theory.

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Extra resources for Algorithmic Learning Theory: 26th International Conference, ALT 2015, Banff, AB, Canada, October 4-6, 2015, Proceedings

Example text

An increasingly popular class of latent variable models are mixed membership models, where each datum may belong to several different latent classes simultaneously. LDA is one such model for 26 A. Anandkumar et al. the case of document modeling; here, each document corresponds to a mixture over topics (as opposed to just a single topic). The distribution over such topic mixtures is a Dirichlet distribution Dir(α) with parameter vector α ∈ Rk++ with strictly positive entries; its density over the probability simplex Δk−1 := {v ∈ k Rk : vi ∈ [0, 1]∀i ∈ [k], i=1 vi = 1} is given by Γ (α0 ) pα (h) = k i=1 k Γ (αi ) i=1 i −1 hα , i h ∈ Δk−1 where α0 := α1 + α2 + · · · + αk .

We repeat the experiment 10 times to obtain the recovery rate (number of success/10) for each value of m (number of measurements). Figure 1b plots the recovery rate of different approaches for different m. Clearly, the rank-one based measurements have similar recovery rate and measurement complexity as the RIP based operators. However, our rank-one operator based methods are much faster than the corresponding methods for the RIP-based measurement scheme. Finally, in Figure 2, we validate our theoretical analysis on the measurement complexity by showing the recovery rate for different d and m.

Furthermore, the method c Springer International Publishing Switzerland 2015 K. Chaudhuri et al. ): ALT 2015, LNAI 9355, pp. 19–38, 2015. 1007/978-3-319-24486-0 2 20 A. Anandkumar et al. of moments can be viewed as complementary to the maximum likelihood approach; simply taking a single step of Newton-Ralphson on the likelihood function starting from the moment based estimator [22] often leads to the best of both worlds: a computationally efficient estimator that is (asymptotically) statistically optimal.

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